Mineral wools are the most widely used building insulation material worldwide. Annually, 2.5 million tonnes of mineral wool waste are generated in the EU alone, and this is a largely unutilised material that is landfilled or incinerated. However, mineral wool wastes are promising precursors for production of alkali-activated cementitious binders due to their favourable chemical and mineralogical composition and high surface area. Alkali-activation is therefore a valuable route for valorisation of large quantities of mineral wool waste. This study resolves the phase assemblage and nanostructure of reaction products formed upon alkali activation of stone wool and glass wool by sodium hydroxide and sodium silicate solutions with X-ray diffraction, electron microscopy and solid state nuclear magnetic resonance spectroscopy experiments probing 27Al and 29Si. The stone wool-based alkali-activated binder comprises an amorphous sodium- and aluminium-substituted calcium silicate hydrate (C-(N-)A-S-H) gel, an amorphous sodium aluminosilicate hydrate (N-A-S-H) gel and small amounts of the layered double hydroxide phase quintinite and zeolite F. The glass wool-based alkali-activated binder comprises an amorphous Ca- and Al-substituted sodium silicate (N-(C-)(A-)S–H) gel. Gel chemical composition and reaction kinetics of alkali-activated mineral wools are shown to be dependent on the activating solution chemistry, with reaction rate and extent promoted by inclusion of a source of soluble Si in the reaction mixture. This work provides the most advanced description of the chemistry and structure of alkali-activated mineral wools to date, yielding new insight that is essential in developing valorisation pathways for mineral wools by alkali activation and providing significant impetus for development of sustainable construction materials.